Question: Simplify the following expression: $ n = \dfrac{2}{7} + \dfrac{2}{-8a + 1} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-8a + 1}{-8a + 1}$ $ \dfrac{2}{7} \times \dfrac{-8a + 1}{-8a + 1} = \dfrac{-16a + 2}{-56a + 7} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{2}{-8a + 1} \times \dfrac{7}{7} = \dfrac{14}{-56a + 7} $ Therefore $ n = \dfrac{-16a + 2}{-56a + 7} + \dfrac{14}{-56a + 7} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{-16a + 2 + 14}{-56a + 7} $ $n = \dfrac{-16a + 16}{-56a + 7}$ Simplify the expression by dividing the numerator and denominator by -1: $n = \dfrac{16a - 16}{56a - 7}$